Systems and methods for preserving phase information in diffusion-weighted magnetic resonance imaging

ABSTRACT

Systems and methods for performing diffusion-weighted magnetic resonance imaging (“MRI”), including reconstructing and analyzing images, while preserving phase information that is traditionally discarded in such applications, are provided. For instance, background phase variations are eliminated, which enables complex-valued data analysis without the usual noise bias. As a result, the systems and methods described here provide an image reconstruction that enables true signal averaging, which increases signal-to-noise ratio (“SNR”) and allows higher contrast in diffusion model reconstructions without a magnitude bias.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/005,599, filed on May 30, 2014, and entitled“SYSTEMS AND METHODS FOR PRESERVING PHASE INFORMATION INDIFFUSION-WEIGHTED MAGNETIC RESONANCE IMAGING.”

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under MH093765,EB015896, and EB012107 awarded by the National Institutes of Health. Thegovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

The field of the invention is systems and methods for magnetic resonanceimaging (“MRI”). More particularly, the invention relates to systems andmethods for preserving phase information in diffusion-weighted MRI,including diffusion tensor imaging (“DTI”), diffusion spectrum imaging(“DSI”), q-ball imaging (“QBI”), and the like.

Diffusion-weighted MRI (“dMRI”) is a useful too for providing valuableneuroscientific and clinical information. In dMRI, magnetic resonancesignals are sensitized to anisotropic water diffusion through localizedsignal attenuation. Diffusion MRI models, such as DTI, DSI, and QBI canuse this diffusion weighting dependent signal attenuation to obtainstructural tissue information.

A magnetic resonance signal is complex-valued and, therefore, includesboth magnitude and phase components. During the diffusion encodingprocess, which is realized by applying magnetic field gradients inspecific directions, physiological and other motion sources can causesmooth phase variations across the acquired complex image. Examples ofsuch physiological motion sources includes brain motion, cardiac motion,and respiratory motion.

These background phase variations do not have an impact on the magnitudeof the image; thus, diffusion MRI commonly uses magnitude-only images,which are insensitive to these background phase variations. A drawbackof using magnitude-only images arises, however, when multiple suchimages are combined in some way. For example, if the multiple images arecombined (e.g., added) and used for model fitting or signal averaging,the magnitude noise tends to accumulate in a way that zero-mean noise(where half the fluctuations are positive and half are negative) doesnot. This accumulation of noise is generally not an issue if thesignal-to-noise ratio (“SNR”) of the acquired image is high because thedistribution of noise approximates a Gaussian distribution in suchcases. In diffusion-weighted MRI and other low SNR modalities, however,signal averaging can accumulate non-Gaussian noise, which results inbiased data points at low signal intensities.

Thus, in these low signal-to-noise ratio (“SNR”) cases, where many lowSNR images are combined, there is a severe penalty to combiningmagnitude images compared to complex images. This is exactly the regimein which diffusion MRI analysis is situated. Namely, hundreds of low-SNRmagnitude images are typically acquired with different diffusiondirections, after which these images are used as the source to variouscomputed images. As a result, diffusion modeling of signal gets lessaccurate in low SNR regions because noise has a strong influence onsignal attenuation. This influence of the noise leads to incorrect orbiased model fits.

Combining low SNR magnitude images in an attempt to improve SNR, such asby using signal averaging, is also problematic because the signalaveraging assumes a Gaussian noise distribution with a zero mean. But,noise in magnitude data follows a non-central chi-square distributionwith a non-zero mean. As a result, the signal averaging leads to astrong influence of noise and an artifact in terms of signal bias,yielding low contrast in averaged images. For complex-valued signals,averaging is only a valid concept if carried out in the complex domain,which is not directly possible because background phase contaminationdestroys signal coherence of the phase.

A recent attempt at reducing the background phase contamination indiffusion-weighted MRI was discussed by S. J. Holdsworth, et al., in“Diffusion tensor imaging (DTI) with retrospective motion correction forlarge-scale pediatric imaging,”J. Magn. Reson. Imaging, 2012;36:961-971. In this approach, the acquired k-space data is apodizedusing a triangular window filter having a fixed size (e.g., 25 percentof k-space). Because this approach removes the higher spatialfrequencies in k-space, spatial resolution in the resultant images isreduced. This reduction in spatial resolution can result in missingfast-changing phase variations, such as those that typically occur attissue borders or where significant subject motion results in rapidphase changes. As a consequence, these fast phase variations may not beestimated or otherwise removed. Another drawback of this method is thatstronger diffusion weightings (i.e., higher b-values) result in morephase variations, which also might not be estimated or otherwise removedbased on the apodization of k-space.

Another attempt at reducing the background phase contamination indiffusion-weighted MRI was proposed by J. I. Sperl, et al., in “PhaseSensitive Reconstruction in Diffusion Spectrum Imaging Enabling VelocityEncoding and Unbiased Noise Distribution,” In Proceedings of the 21stannual meeting of ISMRM, Salt Lake City, 2013; p. 2054. This approachutilized a low-order polynomial fitting and subtraction of the imagephase across image space, and a linear fitting and subtraction of thephase evolution across diffusion space (i.e., “q-space”). The low-orderpolynomial fitting used in this approach may be valid for low b-values,but it is not a reliable approach when larger b-values are used becausewith higher b-values, background phase contamination becomesincreasingly complicated and therefore harder to fit with a low-orderpolynomial term. The polynomial fitting is also not as reliable atresolving phase jumps at tissue borders. Another drawback with thismethod is that a large range of q-space has to be covered (i.e.,multiple diffusion directions and weightings need to be acquired).

After removing the polynomial phase term in image space, a linear termacross the different b-values (i.e., in q-space) is estimated using alinear fitting. This two-step approach removes the linear term after thebackground phase is removed in the first step. There is reason tobelieve, however, that the polynomial phase term and the linear phaseterm are not independent of each other; thus, a two-step approach ofestimating and removing these effects is likely to introduce errors inthe final reconstruction.

In light of the foregoing, there remains a need to provide areconstruction algorithm for diffusion-weighted MRI that is capable ofreliably estimating and removing undesired background phase variations,such that complex-valued data can be utilized in diffusion analyses,such as diffusion tensor calculations and tractography methods.

SUMMARY OF THE INVENTION

The present invention overcomes the aforementioned drawbacks byproviding a method for producing an image, in which background phasevariations are removed, from data acquired using a magnetic resonanceimaging (“MRI”) system. Diffusion-weighted data that was acquired withan MRI system is provided, from which a complex-valued image isreconstructed. Background phase variations are estimated based on thereconstructed complex-valued image. A complex-valued, phase-correctedimage is then produced by removing the estimated background phasevariations from the reconstructed complex-valued image.

The foregoing and other aspects and advantages of the invention willappear from the following description. In the description, reference ismade to the accompanying drawings that form a part hereof, and in whichthere is shown by way of illustration a preferred embodiment of theinvention. Such embodiment does not necessarily represent the full scopeof the invention, however, and reference is made therefore to the claimsand herein for interpreting the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart setting forth the steps of an example method forestimating and removing background phase variation from complex-valueddata, such as diffusion-weighted data; and

FIG. 2 is a block diagram of an example of a magnetic resonance imaging(“MRI”) system.

DETAILED DESCRIPTION OF THE INVENTION

Described here are systems and methods for performing diffusion-weightedmagnetic resonance imaging (“MRI”), including reconstructing andanalyzing images, while preserving phase information that istraditionally discarded in such applications. For instance, the systemsand methods described here are capable of eliminating background phasevariations and, therefore, can enable complex-valued data analysiswithout undesirable noise bias. As a result, the systems and methodsdescribed here provide an image reconstruction that enables true signalaveraging, which increases signal-to-noise ratio (“SNR”) and allowshigher contrast in diffusion model reconstructions without a magnitudebias.

In general, the systems and methods described here model the spatialdependence of the undesired, background phase variations in a low SNRdiffusion-weighted sub-image. This undesired signal phase has a complexspatial pattern, which is different from shot-to-shot based onrespiratory effects and other micro-motions of the tissue, subject, orboth. Although the undesired phase signal has a complicated spatialpattern, the undesired signal phase is separable from the true thermalnoise phase, which is uncorrelated from pixel-to-pixel. As a result, theundesired signal phase can be subtracted, or otherwise removed, from theacquired signals to leave only the thermal noise phase. Removing theundesired signal phase leaves a complex image whose real part containsthe image signal plus the real part of the thermal noise, and whoseimaginary component contains only the imaginary component of the thermalnoise.

This complex image can be used for the analysis of the diffusioninformation, such as neural fiber orientation and diffusion parametersin healthy or clinical populations (e.g., brain stroke, hemorrhage),rather than the traditional approach of analyzing a magnitude-onlyimage. As a result, the magnitude noise accumulation problem describedabove is avoided. If desired, the imaginary component can even be set tozero to reduce the effect of the thermal noise.

Complex-valued diffusion-weighted magnetic resonance data iscontaminated with background phase variations that arise from magneticfield inhomogeneities, eddy currents, respiratory effects, cardiacmotion, and coherent motion, such as brain perfusion. As a result ofthese variations, complex-valued MRI signals, I, are a superposition ofthe underlying magnitude signal, I₀; a tissue phase, φ₀; and a spatiallysmooth background phase, φ_(BG) that varies for each slice, diffusiondirection, and time point. The complex-valued MRI signals can be modeledas,

I(r)=I ₀(r)e ^(iφ) ⁰ ^((r)) e ^(iφ) ^(BG) ^((r))  (1).

In a standard reconstruction of magnitude images, the background phasevariations do not have an impact on the final image because the signalphase information is removed from the images. In order to use fullcomplex data in diffusion MRI applications, the background phasevariations need to be removed. Removing these background phasevariations results in a coherent signal in the real part of the data.

The image reconstruction described here employs a denoising algorithm,which may include a filtering algorithm, to estimate the backgroundphase, φ_(BG). By estimating this phase, it can be removed fromcomplex-valued images, thereby preserving useful phase information thatis traditionally discarded.

Background phase is generally smooth in image space, with jumping pointsat tissue borders. Based on its smoothness in image space, thebackground phase can be estimated from each diffusion-weighted datasetby using an appropriate denoising algorithm. If denoising parameters areset correctly, the phase of the denoised dataset resembles the diffusionbackground phase, φ_(BG).

In some embodiments, an l₁-regularized total variation (“TV”) denoisingalgorithm can be used to estimate the background phase, φ_(BG). Forinstance, such a denoising algorithm can have the following form:

$\begin{matrix}{{\min\limits_{I_{BG}}\{ {{{I_{BG} - I}}_{2}^{2} + {\lambda {{\nabla_{r}I}}_{1}}} \}};} & (2)\end{matrix}$

where I_(BG) is the component of the denoised magnetic resonance signalsthat is attributable to the background phase, φ_(BG). It will beappreciated by those skilled in the art that denoising algorithms otherthan TV denoising can readily be used to estimate the background phase,φ_(BG), without departing from the scope of the invention. As oneexample, median filtering can also be used to estimate the backgroundphase, φ_(BG).

The denoised data follow a smooth phase variation, φ_(BG), which can beused for pointwise background phase correction in each voxel to form aphase corrected dataset, I_(corr), according to

$\begin{matrix}{I_{corr} = {{I \cdot ( \frac{I_{BG}^{*}}{I_{BG}} )} = {I \cdot {^{{- }\; \varphi_{BG}}.}}}} & (3)\end{matrix}$

Referring now to FIG. 1, a flowchart is illustrated setting forth thesteps of an example method for reconstructing and processing adiffusion-weighted image for use in diffusion analyses, includingdiffusion tensor calculations and fiber tractography computations.

First, complex-valued diffusion-weighted data are acquired, or otherwiseprovided, as indicated at step 102. The data can be acquired using anysuitable diffusion-weighted MRI technique, including diffusion tensorimaging (“DTI”), diffusion spectrum imaging (“DSI”), and q-ball imaging(“QBI”). In some instances, the data can already be acquired and thuscan be provided by retrieving the already acquired data from storage. Byway of example, data may be acquired using a twice-refocused DSI pulsesequence, in which data are acquired with isotropic resolution of2.4×2.4×2.4 mm³ and to cover a half spherical diffusion q-space with 256diffusion directions using a maximum b-value of b=7000 s/mm². After thedata are acquired, or otherwise provided, complex-valued images arereconstructed, as indicated at step 104. In some embodiments,reconstructing the complex-valued images may include reconstructing lowsignal-to-noise ratio (“SNR”) sub-images that are also complex-valued.

The undesired, background phase is estimated from the reconstructedimages, as indicated at step 106. For instance, the background phase canbe estimated by using a denoising algorithm that is designed to extractthe undesired background phase. In some embodiments, the denoisingalgorithm is applied to low SNR sub-images. Because background phasevaries significantly between measurements, the denoising algorithm ispreferably applied in two-dimensional space for each slice if the slicesare acquired separately. The denoising algorithm can include anl₁-regularized TV denoising algorithm, such as the one described above.The denoising algorithm can also include any number of suitablefiltering algorithms, including a median filtering algorithm.

After the background phase has been estimated, it is removed from thereconstructed images, as indicated at step 108. As one example, thebackground phase can be removed using a multiplicative factor that isbased on the estimated background phase. As another example, thebackground phase can be subtracted from the reconstructed images.

A decision is then made as to whether to maintain the phase-correctedimages as complex-valued images, or whether to keep only the realcomponent of the images, as indicated at decision block 110. If theimages are to be kept as complex-valued images, then the complex-valued,phase-corrected images are stored for later use, as indicated at step112. If, however, only the real component of the phase-corrected imagesis to be kept, the real part of the images is extracted, as indicated atstep 114. As one example, the real part can be extracted by zeroing theimaginary part, as described above. After the real parts of thephase-corrected images have been extracted, they are stored asreal-valued, phase-corrected images, as indicated at step 116.

The stored, phase-corrected images can then be processed using thedesired diffusion MRI analysis, which may include computing diffusiontensors are related metrics, performing tractography, and so on.

Thus, the reconstruction method described above provides a way toeliminate undesirable noise bias inherent in magnitude images producedfrom low SNR MRI data, such as diffusion MRI, by enabling the use ofcomplex-valued or real-valued data. In some embodiments, thereconstruction method can be applied to non-diffusion-weighted MRI data,such as data acquired using dynamic susceptibility contrast imagingtechniques. As noted above, the output of the reconstruction can eitherbe complex-valued or real-valued. Having such data, averaging can beemployed to increase SNR. Furthermore mathematical models based onsignal intensity will perform more accurately in low SNR datasets.

In some embodiments, the reconstruction method described above can becombined with computational optimization algorithms and statistical dataanalysis in such a way that the phase-corrected signals will follow anexpected optimal distribution of values. For example, in the optimalcase, the imaginary component of the corrected signals will not containany information except for Gaussian noise and, therefore, be normallydistributed. As another example, if the phase correction corrects forboth background phase and image noise, the real values of the data wouldstart to follow a non-zero chi-square distribution. If such desirableand undesirable characteristics of the corrected data are considered, itis possible to implement an online optimization in such a way that theimaginary data will optimally follow a Gaussian distribution and thereal-valued data will not follow a chi-square distribution. Such anoptimization will result in optimal phase correction of the backgrounddata. The suggested algorithm using TV background estimation is moreflexible in terms of achieving such an optimized phase correction.

Referring particularly now to FIG. 2, an example of a magnetic resonanceimaging (“MRI”) system 200 is illustrated. The MRI system 200 includesan operator workstation 202, which will typically include a display 204;one or more input devices 206, such as a keyboard and mouse; and aprocessor 208. The processor 208 may include a commercially availableprogrammable machine running a commercially available operating system.The operator workstation 202 provides the operator interface thatenables scan prescriptions to be entered into the MRI system 200. Ingeneral, the operator workstation 202 may be coupled to four servers: apulse sequence server 210; a data acquisition server 212; a dataprocessing server 214; and a data store server 216. The operatorworkstation 202 and each server 210, 212, 214, and 216 are connected tocommunicate with each other. For example, the servers 210, 212, 214, and216 may be connected via a communication system 240, which may includeany suitable network connection, whether wired, wireless, or acombination of both. As an example, the communication system 240 mayinclude both proprietary or dedicated networks, as well as opennetworks, such as the internet.

The pulse sequence server 210 functions in response to instructionsdownloaded from the operator workstation 202 to operate a gradientsystem 218 and a radiofrequency (“RF”) system 220. Gradient waveformsnecessary to perform the prescribed scan are produced and applied to thegradient system 218, which excites gradient coils in an assembly 222 toproduce the magnetic field gradients G_(x), G_(y), and G_(z) used forposition encoding magnetic resonance signals. The gradient coil assembly222 forms part of a magnet assembly 224 that includes a polarizingmagnet 226 and a whole-body RF coil 228.

RF waveforms are applied by the RF system 220 to the RF coil 228, or aseparate local coil (not shown in FIG. 2), in order to perform theprescribed magnetic resonance pulse sequence. Responsive magneticresonance signals detected by the RF coil 228, or a separate local coil(not shown in FIG. 2), are received by the RF system 220, where they areamplified, demodulated, filtered, and digitized under direction ofcommands produced by the pulse sequence server 210. The RF system 220includes an RF transmitter for producing a wide variety of RF pulsesused in MRI pulse sequences. The RF transmitter is responsive to thescan prescription and direction from the pulse sequence server 210 toproduce RF pulses of the desired frequency, phase, and pulse amplitudewaveform. The generated RF pulses may be applied to the whole-body RFcoil 228 or to one or more local coils or coil arrays (not shown in FIG.2).

The RF system 220 also includes one or more RF receiver channels. EachRF receiver channel includes an RF preamplifier that amplifies themagnetic resonance signal received by the coil 228 to which it isconnected, and a detector that detects and digitizes the I and Qquadrature components of the received magnetic resonance signal. Themagnitude of the received magnetic resonance signal may, therefore, bedetermined at any sampled point by the square root of the sum of thesquares of the I and Q components:

M=√{square root over (I ² +Q ²)}  (4);

and the phase of the received magnetic resonance signal may also bedetermined according to the following relationship:

$\begin{matrix}{\phi = {{\tan^{- 1}( \frac{Q}{I} )}.}} & (5)\end{matrix}$

The pulse sequence server 210 also optionally receives patient data froma physiological acquisition controller 230. By way of example, thephysiological acquisition controller 230 may receive signals from anumber of different sensors connected to the patient, such aselectrocardiograph (“ECG”) signals from electrodes, or respiratorysignals from a respiratory bellows or other respiratory monitoringdevice. Such signals are typically used by the pulse sequence server 210to synchronize, or “gate,” the performance of the scan with thesubject's heart beat or respiration.

The pulse sequence server 210 also connects to a scan room interfacecircuit 232 that receives signals from various sensors associated withthe condition of the patient and the magnet system. It is also throughthe scan room interface circuit 232 that a patient positioning system234 receives commands to move the patient to desired positions duringthe scan.

The digitized magnetic resonance signal samples produced by the RFsystem 220 are received by the data acquisition server 212. The dataacquisition server 212 operates in response to instructions downloadedfrom the operator workstation 202 to receive the real-time magneticresonance data and provide buffer storage, such that no data is lost bydata overrun. In some scans, the data acquisition server 212 does littlemore than pass the acquired magnetic resonance data to the dataprocessor server 214. However, in scans that require information derivedfrom acquired magnetic resonance data to control the further performanceof the scan, the data acquisition server 212 is programmed to producesuch information and convey it to the pulse sequence server 210. Forexample, during prescans, magnetic resonance data is acquired and usedto calibrate the pulse sequence performed by the pulse sequence server210. As another example, navigator signals may be acquired and used toadjust the operating parameters of the RF system 220 or the gradientsystem 218, or to control the view order in which k-space is sampled. Instill another example, the data acquisition server 212 may also beemployed to process magnetic resonance signals used to detect thearrival of a contrast agent in a magnetic resonance angiography (“MRA”)scan. By way of example, the data acquisition server 212 acquiresmagnetic resonance data and processes it in real-time to produceinformation that is used to control the scan.

The data processing server 214 receives magnetic resonance data from thedata acquisition server 212 and processes it in accordance withinstructions downloaded from the operator workstation 202. Suchprocessing may, for example, include one or more of the following:reconstructing two-dimensional or three-dimensional images by performinga Fourier transformation of raw k-space data; performing other imagereconstruction algorithms, such as iterative or backprojectionreconstruction algorithms; applying filters to raw k-space data or toreconstructed images; generating functional magnetic resonance images;calculating motion or flow images; and so on.

Images reconstructed by the data processing server 214 are conveyed backto the operator workstation 202 where they are stored. Real-time imagesare stored in a data base memory cache (not shown in FIG. 2), from whichthey may be output to operator display 212 or a display 236 that islocated near the magnet assembly 224 for use by attending physicians.Batch mode images or selected real time images are stored in a hostdatabase on disc storage 238. When such images have been reconstructedand transferred to storage, the data processing server 214 notifies thedata store server 216 on the operator workstation 202. The operatorworkstation 202 may be used by an operator to archive the images,produce films, or send the images via a network to other facilities.

The MRI system 200 may also include one or more networked workstations242. By way of example, a networked workstation 242 may include adisplay 244; one or more input devices 246, such as a keyboard andmouse; and a processor 248. The networked workstation 242 may be locatedwithin the same facility as the operator workstation 202, or in adifferent facility, such as a different healthcare institution orclinic.

The networked workstation 242, whether within the same facility or in adifferent facility as the operator workstation 202, may gain remoteaccess to the data processing server 214 or data store server 216 viathe communication system 240. Accordingly, multiple networkedworkstations 242 may have access to the data processing server 214 andthe data store server 216. In this manner, magnetic resonance data,reconstructed images, or other data may be exchanged between the dataprocessing server 214 or the data store server 216 and the networkedworkstations 242, such that the data or images may be remotely processedby a networked workstation 242. This data may be exchanged in anysuitable format, such as in accordance with the transmission controlprotocol (“TCP”), the internet protocol (“IP”), or other known orsuitable protocols.

The present invention has been described in terms of one or morepreferred embodiments, and it should be appreciated that manyequivalents, alternatives, variations, and modifications, aside fromthose expressly stated, are possible and within the scope of theinvention.

1. A method for producing an image, in which background phase variationsare removed, from data acquired using a magnetic resonance imaging (MRI)system, the steps of the method comprising: (a) providingdiffusion-weighted data that was acquired with an MRI system; (b)reconstructing a complex-valued image from the provided data; (c)estimating background phase variations based on the reconstructedcomplex-valued image; and (d) producing a complex-valued,phase-corrected image by removing the estimated background phasevariations from the reconstructed complex-valued image.
 2. The method asrecited in claim 1, wherein step (c) includes estimating the backgroundphase variations using at least one of a smoothing algorithm and adenoising algorithm that is designed to produce an image having a phasecomponent equal to the background phase variations.
 3. The method asrecited in claim 2, wherein the denoising algorithm includes anL1-regularized total variation minimization.
 4. The method as recited inclaim 2, wherein the at least one of a smoothing algorithm and adenoising algorithm comprises applying a filter to the reconstructedimage.
 5. The method as recited in claim 4, wherein the filter is amedian filter.
 6. The method as recited in claim 1, further comprisingproducing a real-valued, phase-corrected image by extracting areal-valued component of the complex-valued, phase-corrected image. 7.The method as recited in claim 1, wherein step (d) includes subtractingthe estimated background phase variations from the reconstructedcomplex-valued image.
 8. The method as recited in claim 1, wherein step(d) includes applying a multiplicative factor based on the estimatedbackground phase variations to the reconstructed complex-valued images.9. The method as recited in claim 8, wherein the multiplicative factoris based on a ratio between a complex conjugate of the estimatedbackground phase variations and a magnitude of the estimated backgroundphase variations.
 10. A method for producing an image, in whichbackground phase variations are removed, from data acquired using amagnetic resonance imaging (MRI) system, the steps of the methodcomprising: (a) providing data that was acquired with an MRI system; (b)reconstructing a complex-valued image from the provided data; (c)estimating background phase variations based on the reconstructedcomplex-valued image; and (d) producing a phase-corrected image byremoving the estimated background phase variations from thereconstructed complex-valued image.
 11. The method as recited in claim10, wherein step (c) includes estimating the background phase variationsusing at least one of a smoothing algorithm and a denoising algorithmthat is designed to produce an image having a phase component equal tothe background phase variations.
 12. The method as recited in claim 11,wherein the denoising algorithm includes an L1-regularized totalvariation minimization.
 13. The method as recited in claim 11, whereinthe at least one of the smoothing algorithm and the denoising algorithmcomprises applying a filter to the reconstructed image.
 14. The methodas recited in claim 13, wherein the filter is a median filter.
 15. Themethod as recited in claim 10, wherein the data provided in step (a) isdiffusion-weighted data.
 16. The method as recited in claim 10, whereinthe data provided in step (a) is dynamic susceptibility-weighted data.